The lowest common ancestor (LCA) of two nodes U and V in a tree is the deepest node that has both U and V as descendants.
A binary search tree (BST) is recursively defined as a binary tree which has the following properties:
- The left subtree of a node contains only nodes with keys less than the node’s key.
- The right subtree of a node contains only nodes with keys greater than or equal to the node’s key.
- Both the left and right subtrees must also be binary search trees.
Given any two nodes in a BST, you are supposed to find their LCA.
Each input file contains one test case. For each case, the first line gives two positive integers: M (≤ 1,000), the number of pairs of nodes to be tested; and N (≤ 10,000), the number of keys in the BST, respectively. In the second line, N distinct integers are given as the preorder traversal sequence of the BST. Then M lines follow, each contains a pair of integer keys U and V. All the keys are in the range of int.
For each given pair of U and V, print in a line
LCA of U and V is A. if the LCA is found and
A is the key. But if
A is one of U and V, print
X is an ancestor of Y. where
Y is the other node. If U or V is not found in the BST, print in a line
ERROR: U is not found. or
ERROR: V is not found. or
ERROR: U and V are not found..
LCA of 2 and 5 is 3.
- pre 是前序遍历
- sets 是所有节点的集合
num_test, num_nodes = list(map(int, input().split()))